Determine the length of AB and AD sides from ABCD parallelogram with AD = 3/5AB if ABCD's perimeter is 11.2.
4 Answers | Add Yours
ABCD is a parallelogram, so the opposite sides are equal and parallel.
We note that we'll have to have the same denominator on both sides of equality, the denominator being 5.
5*5.6cm= 5*AB + 3*AB
The answer to this is that AB is 3.5 and AD is 2.1. Here is how to find this.
We know that the perimeter of the parallelogram can be found by multiplying both sides by 2 and then adding the products.
We know then that two sides are equal to 2AB.
And we know that the other two sides are equal to 6/5 AB.
So now we can say that
2AB + 6/5AB = 11.2
This means that
3.2AB = 11.2
When we divide this, we find that
AB = 3.5
To find AD, we do the following:
AD = 3/5(3.5)
This multiplies out to
AD = 2.1
ABCD is a parallelogram. AD = (3/5)AB
The perimeter is 1.2.
To determine AB and AD.
Let AB =x .
Then AD = (3/5)x = 0.6x.
Since ABCD is a parallelogram AB = CD and AD = BC.
Therefore , the perimeter p = 2x+2*0.6x = 3.2x which is equal to 11.2.
So 3.2x = 11.2
x = 11.2/3.2 = 3.5.
So AB = 3.5.
Therefore AD = (3/5)AD = 3*3.50/5 = 2.1.
For a parallelogram the opposite sides are equal. So here we have AB = DC and AD = BC.
Now we know that AD = (3 / 5)* AB. And the perimeter of the parallelogram is 11.2.
AB + BC + CD + DA = 11.2
=> AB + (3 / 5)* AB + AB + (3 / 5)* AB = 11.2
=> AB *( 1+ 3/5 +1 + 3/5) = 11.2
=> AB = 11.2 / 3.2
=> AB = 3.5
AD = (3 / 5)* AB
=> AD = (3 / 5)* 3.5 = 2.1
Therefore AB is 3.5 and AD is 2.1
Join to answer this question
Join a community of thousands of dedicated teachers and students.Join eNotes